Magnets and the magnetic field Electric currents create magnetic fields Magnetic fields of wires, loops, and solenoids Magnetic forces on charges and currents Magnets and magnetic materials Chapter 24 Magnetic Fields and Forces Topics: Sample question: This image of a patient’s knee was made with magnetic fields, not x rays. How can we use magnetic fields to visualize the inside of the body? Slide 24-1

Key Points Three types of magnetic interactions 1.no interaction with either pole of a magnet => object is non-magnetic 2.attracted to both poles of a magnet => object is magnetic 3.Attracted to one pole and repelled by the other pole => object is a magnet Magnetic field vector from a bar magnet is a super position of the magnetic field vectors from the N and S poles: Vector from N pole points away from N pole Vector from S pole points towards S pole Field lines form complete loops inside and outside of magnet Field lines outside magnet go from N to S poles Field lines inside magnet go from S to N poles Magnetic Field vectors at a point are tangential to Magnetic Field Lines

3-D Arrows, Cross Products, and Right Hand Rule 1 Slide 24-2 Showing vectors in 3D Cross Product For direction use Right-hand rule 1 Right-hand rule 1 (RHR 1) => for finding direction of cross-product vector (Cross-Product Rule) 1.Point right hand in the direction of the first vector (vector A) 2.Rotate your right hand until you can point your fingers in the direction of the second vector (vector B) 3.Thumb points in direction the cross-product vector (vector C)

Right Hand Rules for Magnetism Right-hand rule 1 (RHR 1) => for finding magnetic force F B = q*v_vector x B_vector (Cross-Product Rule) 1.Point right hand in the direction the charges are moving (current or velocity) 2.Rotate your right hand until you can point your fingers in the direction of the magnetic Field 3.Thumb points in direction of force for + charge Force is in opposite direction for - charges Right-hand rule 2 (RHR 2) => Finding direction of B from I Point thumb of right hand in direction of current I, B-field lines curl in direction of fingers Right-hand rule 3 (RHR 3) => Finding direction of current in a loop from direction of B-field Point thumb of right hand in direction of B-field Fingers of right hand curl in direction of current Slide 24-2

Drawing Field Lines of a Bar Magnet Slide 24-10

Magnetic Fields Produced by Bar Magnets A single bar magnet (closeup) Slide 24-11

Magnetic Fields Produced by Bar Magnets Two bar magnets, unlike poles facing Two bar magnets, like poles facing Slide 24-12

Magnetic Fields from Two Magnets Bar Magnets A and B are placed at right angles. Two compasses, X and Y are placed so that they are equidistant from the two magnets as shown A.) The arrow in compass X indicates the direction in which the North pole of the compass is pointing. Indicate the North and South ends of both magnets in the diagram B.) Draw an arrow in compass Y to show the direction in which the North pole of the compass needle would point. Slide 24-2

Electric Currents Also Create Magnetic Fields A long, straight wire A current loopA solenoid Slide 24-15

The Magnetic Field of a Straight Current-Carrying Wire Slide 24-16

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Representing Vectors and Currents That Are Perpendicular to the Page Slide 24-18

Checking Understanding Point P is 5 cm above the wire as you look straight down at it. In which direction is the magnetic field at P? Slide 24-19

Answer Point P is 5 cm above the wire as you look straight down at it. In which direction is the magnetic field at P? Slide 24-20

Drawing Field Vectors and Field Lines of a Current-Carrying Wire Slide 24-21

Drawing a Current Loop Slide 24-22

The Magnetic Field of a Current Loop Slide 24-23

The Magnetic Field of a Solenoid A short solenoidA long solenoid Slide 24-24

The Magnitude of the Field due to a Long, Straight, Current-Carrying Wire Slide 24-25

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Checking Understanding A.10 A to the right. B.5 A to the right. C.2.5 A to the right. D.10 A to the left. E.5 A to the left. F.2.5 A to the left. The magnetic field at point P is zero. What are the magnitude and direction of the current in the lower wire? Slide 24-27

E.5 A to the left. The magnetic field at point P is zero. What are the magnitude and direction of the current in the lower wire? Slide Answer

The Magnetic Field of a Current Loop Magnetic field at the center of a current loop of radius R Magnetic field at the center of a current loop with N turns Slide 24-29

Example What is the direction and magnitude of the magnetic field at point P, at the center of the loop? Slide 24-30

The Magnetic Field Inside a Solenoid Magnetic field inside a solenoid of length L with N turns. Slide 24-31